電磁成形解析

High-speed forming using pulsed strong magnetic fields. Magnetic pressure induced by eddy currents. Tube expansion and sheet forming for automotive parts.

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrices and construct the global stiffness equation.

We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

We solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Founded in Sweden in 1986. Started as FEMLAB with MATLAB integration, later renamed to COMSOL. Strong in multiphysics.

Developed by Japan's JSOL Corporation. An electromagnetic field analysis tool specialized for electrical equipment design.

Developed in 1970 by Swanson Analysis Systems Inc. (SASI). Based on APDL (Ansys Parametric Design Language).

When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.

Verifying mesh convergence, validating the appropriateness of boundary conditions, and performing sensitivity analysis of material parameters are extremely important.